How long it takes to train face recognition deep neural network? (rough estimation)
Training time depends on a lot of parameters. Some of them are:


Size of each image (resolution)
Color/Monochrome image (color image has 3 times data if you consider RGB image)
Like you mentioned on the type of DNN.
No. of layers of DNN.
No. of neurons in each layer. 
Total no. of images in the dataset. (2.6 million here)
GPU you are using (you didn't mention which GPU you are using. There are GPUs with wide range of capabilities, to predict the time, you need to know the exact specs of GPU). 
Training time also depends on RAM on your machine and also how fast host PC can transfer data to GPU for processing.
Since you mentioned face recognition, i am assuming you are using CNN, but if you again use fully connected network, training time will change and will obviously increase manifold.


Your task of classification and your database is mostly similar to ILSVRC that uses imagenet database.

Making some reasonable assumptions for the parameters you didn't mention, i feel your task is similar to ILSVRC and i am predicting the training time will be a few days.

Below are the links which mention time of training for ILSVRC.

https://mxnet-tqchen.readthedocs.io/en/latest/tutorials/imagenet_full.html

Below are the details of imagenet database for your comparison

https://en.wikipedia.org/wiki/ImageNet